Recycling augmented Lagrangian preconditioner in an incompressible fluid solver

12/18/2020

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by   Maxim Olshanskii, et al.

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The paper discusses a reuse of matrix factorization as a building block in the Augmented Lagrangian (AL) and modified AL preconditioners for a non-symmetric saddle point linear algebraic systems. The strategy is applied to solve two-dimensional incompressible fluid problems with efficiency rates independent of the Reynolds number. The solver is then tested to simulate a motion of surface fluids, an example of 2D flows motivated by an interest in lateral fluidity of inextensible viscous membranes. Numerical examples include the Kelvin-Helmholtz instability problem posed on the sphere and on the torus.